Meaning and Measure of Inflation Lecture No. 35 Chapter 11 Contemporary Engineering Economics Copyright © 2016

What is Inflation? Definition: The rate at which the general level of prices of goods and services is rising, and subsequently, purchasing power is falling Time Value of Money Earning power Investment opportunity Purchasing power Decrease in purchasing power (inflation) Increase in purchasing power (deflation)

Chapter Opening Story Purchasing Power: The Big Mac Index An indicator of a country’s individual purchasing power. Big Mac prices are calculated by converting the average national Big Mac prices with the latest exchange rate to U.S. dollars. Two dominant factors are Inflation and cost of labor. Source: “The Big Mac Index,” The Economist, January 25, 2014

Inflation: Decrease in Purchasing Power $110 $110 1990 1990 2015 You could buy 50 Big Macs in the year 1990 with $110. You can only buy 23.81Big Macs in the year 2015. +210% $2.20 / unit $4.62 / unit Price change due to inflation The $110 in year 2015 has only $52.38 worth the purchasing power of 1990.

Deflation: Increase in Purchasing Power $100 $100 2012 2012 2015 With $100, you could purchase 27.17gallons of unleaded gasoline in 2012. With $100, you can now purchase 42.55gallons of unleaded gasoline in 2015. −36.14% $3.68 / gallon $2.35 / gallon Price change due to deflation

Inflation Terminology I Producer Price Index:A statistical measure of industrial price change, compiled monthly by the Bureau of Labor Statistics, U.S. Department of Labor Consumer Price Index:A statistical measure of change, over time, of the prices of goods and services in major expenditure groups—such as food, housing, apparel, transportation, and medical care—typically purchased by urban consumers Average Inflation Rate (f):A single average rate that accounts for the effect of varying yearly inflation rates over a period of several years General Inflation Rate (f ): The average inflation rate calculated based on the CPI for all items in the market basket

Consumer Price Index (CPI) Definition: A measure that examines the weighted average prices of a consumer goods and services. How to calculate: Taking price changes for each item in the market basket of goods and services and averaging them. CPI (Old measure) − Base Period = 1967 1967: 100 2015: 712.35 (May) CPI (New measure) − Base Period (1982–84) 1982–84: 100 2015: 237.85 (May)

Selected Price Indexes

Average Inflation Rate (f ) Given: Base Price = $100 (year 0) Inflation rate (year 1) = 4% Inflation rate (year 2) = 8% Find:Average inflation rate over 2 years Step 1: Find the actual inflated price at the end of year 2. $100 ( 1 + 0.04) ( 1 + 0.08) = $112.32 Step 2: Find the average inflation rate by solving the following equivalence equation. $100 ( 1+ f)2= $112.32 f= 5.98% $100 $112.32 0 1 2

Example 11.1: Average Inflation Rate Sample calculation for average inflation rate for gasoline Given: P = 194.4, F = 304.2, N = 2014–2005 = 9 Find: f

Solution Average inflation rate for gasoline over 9 years

General Inflation Rate (f) Calculation Given: CPI for 2005 = 195.3, CPI for 2014 = 236.4 Find: Formula

Example 11.2: Yearly and Average Inflation Rates Given:Year cost data Find: (1) Yearly and average inflation rates, (2) Average inflation rate (or price index) Year Cost $504,000 1 538,000 2 577,000 3 629,500

Solution

Inflation Terminology II Actual dollars (An): Estimates of future cash flows for year n that take into account any anticipated future changes in amount caused by inflationary or deflationary effects Constant dollars (An’): Estimates of future cash flows for year n in constant purchasing power, independent of the passage of time (or base period)

Finding Actual Dollars Conversion from constant to actual dollars General inflation rate = 5%

Finding Constant Dollars Conversion from actual to constant dollars General inflation rate of 5%

Inflation Terminology III Inflation-free interest rate (i’): an estimate of the true earning power of money when the inflation effects have been removed (also known as real interest rate). Market interest rate (i): an interest rate which takes into account the combined effects of the earning value of capital and any anticipated changes in purchasing power (also known as inflation-adjusted interest rate).

Inflation and Cash Flow Analysis Constant dollar analysis Estimate all future cash flows in constant dollars. Use i’ as an interest rate to find the equivalent worth. Actual dollar analysis Estimate all future cash flows in actual dollars. Use i as an interest rate to find the equivalent worth.

Equivalence Calculations Under Inflation Types of Analysis Method Constant-Dollar Analysis Actual-Dollar Analysis Types of Cash Flows Estimated in Constant Dollars Estimated in Actual Dollars Types of Interest Rate Market Interest Rate (i) Inflation-free Interest Rate (i’)

When to Use Constant Dollar Analysis? In the absence of inflation, all economic analysis up to this point is, in fact, the constant dollar analysis. Constant dollar analysis is common in the evaluation of many long-term public projects, because governments do not pay income taxes. For private sector, income taxes are levied based on the taxable income in actual dollars, so the actual dollar analysis is more common.

Actual Dollars Analysis Method 1: Deflation Method Step 1: Bring all cash flows to have common purchasing power. Step 2: Consider the earning power. Method 2: Adjusted-discount Method Combine Steps 1 and 2 into one step.

Example 11.6: Deflation Method Step 1: Converting actual dollars into constant dollars Step 2: Calculating equivalent present worth

Graphical Overview on Deflation Method Actual Dollars -$75,000 $32,000 $35,700 $32,800 $29,000 $58,000 Constant Dollars -$75,000 $30,476 $32,381 $28,334 $23,858 $45,455 Present Worth $28,218 -$75,000 $21,288 $16,295 $26,761 $27,706 $45,268

Adjusted-Discount Method Discrete compounding Step 1 Step 2 Continuous compounding

Example 11.7: Adjusted-Discounted Method Given: inflation-free interest rate = 0.10, general inflation rate = 5%, and cash flows in actual dollars Find: i and NPW

Graphical Overview on Adjusted Discount Method Actual Dollars -$75,000 $32,000 $35,700 $32,800 $29,000 $58,000 Present Worth $28,218 -$75,000 $21,288 $16,295 $26,761 $27,706 $45,268

Mixed-Dollar Analysis College Savings Plan: Determine the required quarterly contribution Approach: Convert any cash flow elements in constant dollars into actual dollars. Then use the market interest rate to find the equivalent present value. Assume f = 6% and i = 8% compounded quarterly. Age (Current Age = 5 Years Old) Estimated College Expenses in Today’s Dollars College Expenses Converted into Equivalent Actual Dollars 18 (Freshman) $30,000 $30,000(F/P,6%,13) = $63,988 19 (Sophomore) 30,000 30,000(F/P,6%,14) = 67,827 20 (Junior) 30,000(F/P,6%,15) = 71,897 21 (senior) 30,000(F/P,6%,16) = 76,211

Required Quarterly Contributions to College Funds V1 = C(F/A, 2%, 48) V2 = $229,211 Let V1 = V2 and solve for C: C = $2,888.48

Effects of Inflation on Projects with Depreciable Assets Item Effects of Inflation Depreciation expense Salvage value Depreciation expense is charged to taxable income in dollars of declining values; taxable income is overstated, resulting in higher taxes. Inflated salvage value combined with book values based on historical costs results in higher taxable gains. Note: Depreciation expenses are based on historical costs and always expressed in actual dollars.

Example 11.8: Effects of Inflation on Depreciable Assets Given: Reconsider Example 11.1 with: The general inflation = 5% during the next five years is expected to increase by 5% annually. Sales, operating costs, and working capital requirements are assumed to increase accordingly. Depreciation will remain unchanged, but taxes, profits, and thus cash flow will be higher. The firm’s inflation-free interest rate is known to be 15%. Find: Determine the PW of the project.

Solution: Excel Worksheet

Effects of Borrowed Funds Under Inflation Item Effects of Inflation Loan repayments Borrowers repay historical loan amounts with dollars of decreased purchasing power, reducing the debt-financing cost.

Example 11.10: Effects of Inflation on Payments with Financing Given: Borrowing rate = 15.5% General inflation rate = 5% Inflation-free interest rate = 15% Amount of borrowing = $62,500 over 5 years Find: NPW

NPW without borrowing: $38,898 Market interest rate = 0.15 + 0.05 + 0.0075 = 20.75% NPW without borrowing: $38,898 NPW with borrowing: $54,159 The gain in NPW due to debt financing: $15,261

Effects of Inflation on Return on Investment Item Effects of Inflation Rate of Return and NPW Unless revenues are sufficiently increased to keep pace with inflation, tax effects and/or a working capital drain result in lower rate of return or lower NPW.

Example 11.11: IRR Analysis with Inflation IRR in the absence of inflation IRR calculation under inflation

Rate of Return Analysis Under Inflation Principle: True (real) rate of return should be based on constant dollars. If the rate of return is computed based on cash flows in actual dollars, the real rate of return can be calculated as: n Net cash flows in actual dollars Net cash flows in constant dollars 1 2 3 4 -$30,000 13,570 15,860 13,358 13,626 12,336 13,108 10,036 9,307 IRR 31.34% 19.40%

MARR to Use If you use 31.34% as your IRR, you should use a market interest rate (or inflation-adjusted MARR) to make an accept and reject decision. If you use 19.40% as your IRR, you should use an inflation-free interest rate(inflation-free MARR) to make an accept and reject decision. In our example, MARR’ = 20%.

Effects of Inflation on Working Capital Item Effects of Inflation Working capital requirement Known as working capital drain, the cost of working capital increases in an inflationary environment.

Example 11.12: Effects of Inflation on Working Capital

Working Capital Requirements Under Inflation